基于多尺度自适应阶ARMA的混沌序列多步预测

混沌时间序列在自然界以及人们的生产生活中很常见,混沌序列看似杂乱无章但相较于纯随机序列其中蕴含着一些非线性的运动特征,提出一种基于多尺度自适应阶ARMA的混沌时间序列多步预测方法.首先利用自适应噪声的完备经验模态分解(CEEMDAN)对原始混沌序列进行分解,获得不同尺度的固有模态分量(IMF)和残余分量.然后采用经粒子群算法(PSO)进行阶数寻优的自回归移动平均模型(ARMA)对每一个IMF分量进行拟合预测.最后将预测得到的每一个分量相加得到原始混沌序列的预测值.基于Mackay-Glass混沌序列和太阳黑子数混沌序列进行实验分析,实验表明:与ARMA、PSO-ARMA以及CEEMDAN-ARMA方法相比,方法的预测效果有较好的提高,其平均绝对误差(MAE)、均方根误差(RMSE)以及平均绝对百分比误差(MAPE)都有降低.

Multi-step Prediction of Chaotic Time Series Based on Multi-scale Adaptive-order ARMA

Chaotic time series are very common in nature and in people’s production and life.Chaotic sequences seem to be chaotic but contain some nonlinear motion characteristics compared to pure random sequences.Our paper proposes a chaotic time based on multi-scale adaptive ARMA sequence multi-step prediction method.First,the complete empirical mode decomposition(CEEMDAN)of adaptive noise is used to decompose the original chaotic sequence to obtain intrinsic modal components(IMF)and residual components of different scales.Then,the autoregressive moving average model(ARMA),which is optimized by particle swarm optimization(PSO),is used to fit and predict each IMF component.Finally,each component of the prediction is added to obtain the predicted value of the original chaotic sequence.The experimental analysis is based on the Mackay-Glass chaotic sequence and the sunspot number chaotic sequence.The experiment shows that compared with the ARMA,PSO-ARMA and CEEMDAN-ARMA methods,the prediction effect of the method in this paper is better improved,and its average absolute error(MAE),Root Mean Square Error(RMSE)and Mean Absolute Percentage Error(MAPE)are all reduced.